AlgebraAlgebra

8.1-8.3The Rules of Exponents

Exponent TableExponent Table

Meaning ExampleProperty

Product of Powers Property nmnm aaa

Power of a Power Property824 )( xx

Power of a Product Propertymmm baba )( 824 9)3( mm

84424 ))(()( ? xxxxWhy

532 555

nmnm aa )(

532 55)55)(5(555 ? Why

DefinitionsDefinitions

53

BASE

EXPONENT

Examples Using Product of PowersExamples Using Product of Powers

1) x x = 2 4. x 6

2) y y y = 3 4..

3) x y xy = 3 5.

y8

x y42 7

Let’s try three together!

Try these two on your own!

4) 3 3 =. 7

5) (-6) (-6) =4 438

(-6)8

Examples Using Power of a PowerExamples Using Power of a Power

1) (9 ) = 3 4 9 12

2) [(-3) ] = 3 2

(-3)6

Let’s try two together!

Try this one on your own!3) (x ) =2 4 x 8

Examples Using Power of a ProductExamples Using Power of a Product

1) (x y ) = 3 2

x y 6

2) -(2y ) = 4 -16y 12

Let’s try two together!

Try these two on your own!

3) [ a b ] =3

4) (-2y ) =3 4

a b9

16y12

3 9

3

213

3 6127

Using All Three Properties TogetherUsing All Three Properties Together

1) (5x y ) x = 2 . 125x y11

Let’s try one together!

Try this one on your own!

2) (3a b) (2a b ) =2 72a b16

3 3 5

2 24 3 8

9

Exponent TableExponent Table

Meaning ExampleProperty

Product of Powers Property nmnm aaa

Power of a Power Property824 )( xx

Power of a Product Propertymmm baba )( 824 9)3( mm

84424 ))(()( ? xxxxWhy

532 555

nmnm aa )(

532 55)55)(5(555 ? Why

Zero as an Exponent 10 a 12

10

Negative Exponentsn

nn aa

a n-a

1 and

1

Move any exponent across the fraction bar to change the sign of the exponent.

1

4

4

1 and

2

12

2

2-22

Dividing with Exponents 0a nmn

m

aa

a 24

6

55

5

Power of a Quotient Property 0b

m

mm

b

a

b

a

27

8

3

23

Why? See table.

Why? See table.

ExamplesExamples

1) = 32

3 -3

Let’s try two together!

Try this one on your own!

3)

35 =

13

3127=

2) = 3 -2 2

4 [ ] = 1693

423

4

-2

-2

8a b 2a ba b 4b

-13 8

-24-2= 4a b

74

HWHW

• P. 804 #1-28